derivative 7^{x+arccos(x)}

解

導関数

7^{x + a r c c o s (x)}

ln (7) \cdot 7^{x + a r c c o s (x)} (1 - \frac{1}{1 - x ^{2}})

解答ステップ

\frac{d}{d x} (7^{x + a r c c o s (x)})

指数の規則を適用する:

a^{b} = e^{b l n (a)}

7^{x + a r c c o s (x)} = e^{(x + a r c c o s (x)) l n (7)}

= \frac{d}{d x} (e^{(x + a r c c o s (x)) l n (7)})

連鎖法則を適用:

e^{(x + a r c c o s (x)) l n (7)} \frac{d}{d x} ((x + arccos (x)) ln (7))

= e^{(x + a r c c o s (x)) l n (7)} \frac{d}{d x} ((x + arccos (x)) ln (7))

\frac{d}{d x} ((x + arccos (x)) ln (7)) = ln (7) (1 - \frac{1}{1 - x ^{2}})

= e^{(x + a r c c o s (x)) l n (7)} ln (7) (1 - \frac{1}{1 - x ^{2}})

e^{(x + a r c c o s (x)) l n (7)} = 7^{x + a r c c o s (x)}

= ln (7) \cdot 7^{x + a r c c o s (x)} (1 - \frac{1}{1 - x ^{2}})